Wide band ac modulated control networks

ABSTRACT

An electric impedance network for AC carrier frequency control systems which provides optimal arithmetical symmetry in frequency response with respect to the carrier frequency, characterized by having a symmetrical even amplitude response and a symmetrical odd phase response for a substantial frequency band around the carrier frequency.

United States Patent 1 [111 3,764,878 McAuley Oct. 9, 1973 [54] WIDEBAND AC MODULATED CONTROL 3,593,095 7/1971 Davis 318/632 NETWORKS3,601,676 8/1971 Halfhill 318/632 X [76] Inventor: Van A. McAuley, 3529Rosedale Dr., Huntsville, Ala. 35810 [22] Filed: July 14, 1972 [211Appl. No.: 271,958

[52] US. Cl. 318/632 [51] Int. Cl. G05d 23/275 [58] Field of Search318/632 [56] References Cited UNITED STATES PATENTS 2,885,612 5/1959Larsen 318/632 Primary Examiner-Benjamin Dobeck Att0rneyL. D. Wofford,Jr. et al.

[5 7] ABSTRACT An electric impedance network for AC carrier frequencycontrol systems which provides optimal arithmetical symmetry infrequency response with respect to the carrier frequency, characterizedby having a symmetrical even amplitude response and a symmetrical oddphase response for a substantial frequency band around the carrierfrequency.

4 Claims, 9 Drawing Figures 47 47a l l A C AC AC TWO PHASE J46 NETWORKAMPL. MTR

PATENTED 3.764.878

SHEET 2 BF 4 SYNCHRO 42 SET AC TWO AC I X2 NETWORK PHASE 2 MOTOR FIG. 3

CARRIER SIGNAL REFERENCE SIGNAL cus m t 2cos(w t+ LOW x 1 X X (r) PURE x(n MODULATOR 2 7 c (s) 3 1 PASS 4 DEMODULATOR NETWORK FIG. 4

NETWORK FIG. 5

o -wv r c c WIDE BAND AC MODULATED CONTROL NETWORKS ORIGIN OF THEINVENTION The invention described herein was made by an employee of theUnited States Government and may be manufactured and used by or for theGovernment of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

BACKGROUND OF THE INVENTION AC modulated control systems are widely usedin space applications, military applications and industrialapplications. This invention relates to electric systems and networksfor compensation of control signals employed in such systems to the endthat a more suitable performance is obtained, e.g. where controlledapparatus is made to more precisely follow a position command. Moreparticularly, this invention relates to those of such systems whereinthe control signals are in the form of modulation impressed upon acarrier. Typically, the carrier frequency is 60 or 400 Hertz and thecontrol signal modulation is of a substantially lower frequency. It doesfollow that the compensation must be accomplished on frequencies whichare remote from the control signal frequencies. The goal, of course, isto be able to achieve the same compensation to the modulation, ormodulation envelope of the modulated carrier as a lower frequencynetwork would achieve on the control signal alone, that is if it werenot impressed on the carrier.

GENERAL DESCRIPTION OF THE PRIOR ART Of the two basic or standardapproaches to the solution of the problem, one is to demodulate themodulated carrier, apply compensation directly to the demodulatedcontrol signal and then again modulate a carrier with the compensatedcontrol signal. This, of course, requires an additional demodulator andmodulator in addition to the compensating network and thus adds to thecomplexity and expense of the circuitry. The other basic approach is toemploy a compensation network operating directly on the modulatedcarrier. In such instances, three forms are commonly employed, cascadecompensation, feedback compensation and load compensation. In cascadecompensation, to which the present invention is directed, there existsthe problem of providing a network which will operate on the envelope ofthe modulated signal in the same fashion as it would on the modulatingcontrol signal alone. The ideal response is thus simply the unmodulatedcharacteristic shifted from zero to the positive and negative carrierfrequencies. It is well known, however, that such a response or responsecharacteristic cannot be realized exactly for all frequencies.Therefore, the problem may be stated as that of optimal approximation ofthe desired characteristic by a network for a band of frequencies aroundthe carrier frequency, positive and negative.

Up to the present time, the two main methods of solution of the problemutilizing cascade networks have been one of the following. One methodemploys resistance-inductance-capacitance networks characterized by thelow-pass to band-pass impedance frequency transformation, operatingdirectly on impedance elements of the low frequency network to producethe carrier frequency network. The other employs certain types ofresistive-capacitive networks such as those of the twin T or bridged Tconfiguration. These networks, however, have the drawback of yieldingthe desired characteristic for only a very narrow band around thecarrier frequency, plus or minus about five percent, an undesirablysmall band in many instances.

SUMMARY OF THE INVENTION Accordingly, it is an object of the presentinvention to provide a new and improved compensation network which notonly avoids the necessity of the use of auxiliary demodulators andmodulators as aforesaid but provides a wide band solution to the problemof employment of compensation networks operating at carrier frequencies.

It is further object of this invention to provide a compensation networkof the character described wherein there is provided faster response andgreater accuracy of compensation.

Still another object of this invention is to provide improveddemodulator-motor efficiency in motor control networks and thus reducingpower consumption and heating problems.

The aforesaid improved characteristics are obtained in the presentinvention by the arrangement of impedance elements wherein acompensation network is accomplished which is characterized by optimalarithmetical symmetry in frequency response with respect to a carrierfrequency and wherein the network displays a symmetrical even gainresponse but symmetrical odd phase response, both for a substantial bandaround the carrier frequency. The networks are characterized by a lowfrequency to carrier frequency transformation which is a non-impedancefrequency transformation; the transformation does not operate directlyon the impedance elements of the low-frequency network to produce thecarrier frequency network.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a schematic diagram of anelectric control system typical of the system which would employ thepresent invention.

FIG. 2 is an electrical schematic diagram of an alternating currentcircuit as contemplated by the invention in which a control signal andthe modulated output of an AC network to which the control signal isapplied are combined.

FIG. 3 is an electrical block diagram of a simple AC control system.

FIG. 4 is an electrical block diagram of the carrier frequency channelof the control system shown in FIG. 3.

FIG. 5 is an electrical block diagram of the equivalent channel of thatshown in FIG. 4.

FIG. 6 is an electrical schematic diagram of one type of alternatingcurrent network contemplated by the invention.

FIG. 7 is a graph illustrating certain characteristics of the invention.

FIG. 8 is an electrical schematic block diagram of an alternateembodiment of the invention suitable for construction of a ladder typenetwork.

FIG. 9 is an electrical schematic diagram of the twostage ladder networkbasically illustrated in FIG. 8.

DESCRIPTION OF THE PREFERRED EMBODIMENT Referring initially to FIG. I,there is illustrated an alternating current modulated control system forelectrically creating at one location a mechanical movement occurring ordirected at another location. As shown, hand wheel operates rotor 12 ofa synchro or synchro-transformer 14 of a synchro set 15. An AC input towinding 16 of rotor 12 is applied across terminals 18 and 20 with asingle phase alternating current input and the transformer output isprovided by 120 degree phase displaced stator windings 22, 24 and 26.The voltage induced into each of these windings is thus a function ofthe position of hand wheel 10. The output of windings 22, 24 and 26 areconnected to like stator windings 28, 30 and 32 of synchro 34. The rotorwinding 36 of rotor 38 of synchro 34 receives an induced voltage whichis proportional to the difference or error in electrical position ofrotors l2 and 38 and thus of any misalignment of follow-up shaft 40 withrespect to hand wheel 10. The output of winding 36 is applied to theinput of AC network 42 which provides or yields a lead network output,or derivative form of the error voltage. The output of AC network 42 isamplified in AC amplifier 44 and the amplified output used to drive ACtwophase motor 46. A reference phased voltage is applied to terminals 47and 47a. Motor 46 is coupled through gears 50 and 52 to shaft 54 whichpositions it and any work load coupled to it to a position correspondingto the position of hand wheel 10.

A mechanical feedback link from motor 46 is provided through gears 50and 56 and gears 58 and 60 to shaft 40 and thus to rotor 38. In thismanner, rotor 38 is moved in a direction to produce a zero output ofwinding 36, to thus recreate on shafts 48 and 54 the shaft position ofhand wheel 10.

In instances where it is desired to provide both the error signal andthe derivative of the error signal at the input of amplifier 44, thecircuit of FIG. 2 would be connected where AC network 42 alone isconnected in FIG. 1. This circuit would thus be connected with terminals62 and 64 connected to the output of winding 36 (FIG. 1) and outputterminals 66 and 68 connected to the input of amplifier 44.

AC network 42 (FIG. 2) is connected to terminals 62 and 64 through amatching isolation transfonner 70. Potentiometer 72 is connected acrossthe output of an AC network 42 and potentiometer 74 is connected acrossinput terminals 62 and 64. The error voltage, appearing acrosspotentiometer 74, and a selected portion of the output of AC network 42,a derivative of the error voltage, are combined by connecting themovable arm 76 of potentiometer 72 to one side of potentiometer 74. Aselected portion of the error signal is provided in the output acrossterminals 66 and 68 by connecting terminal 66 to movable arm 78 ofpotentiometer 74. Output terminal 68 is connected to the common terminalside of potentiometer 72.

Analysis of Carrier-Frequency Channel of a Modulated Control System andDerivation of Unmodulated Equivalent Transfer Function of the ChannelFIG. 3 is a block diagram ofa simple AC control system or servomechanism. Synchro set serves as both an error-sensing device andmodulator. Two-phase motor 46 serves as the demodulator and drives thesys- @m. FIG. 4 is a block diagram of the forward carrier frequencychannel including modulator 80 and demodulator 82. The transfer functionof AC electrical network 84 (including any AC amplifiers) is G, .(s).FIG. 5 indicates the goal of this derivation, G (s), the transferfunction 86 equivalent of FIG. 4 relating the unmodulated signals X,(s)and X (s).

To derive the required result, the carrier signal, without loss ofgenerality, is cos w where the carrier frequency is w (which is 27rf Thedemodulator reference signal is 2 cos (w t+,,) where 4),, is thedemodulator phase angle which value can be set as required. Thenon-carrier-frequency input signal x (t), FIG. 4, modulates the carriercos w in the modulator resulting in the amplitude modulated signal x (t)(the direct product of the two):

x (t) x,(t) cos w t.

By using the identity cos (n t 5 A (e e equation (I) becomes:

at!) a (8 W x1 (t).

From the Laplace transform of each side of equation From the Laplacetransform of each side of equation where X,(s) a [x (t) and X (s) a [x(t) The relations between the input X (s) and the response transform X-,(s) result by definition:

where G (s) is the transfer function of the AC network of FIG. 3.Substituting equation (4) results in: 30) l( j c) d j c) A (6) Theinverse Laplace transform results in:

Equation (10) shows that the response of the AC network is a modulatedsignal of two components which and W) a a {wa -1 c.( +jw. 1 11.6)

are 90 out of phase. The low-frequency parts of the two components,x,,(t) and x,,(t), are called the inphase component and quadraturecomponent, respectively.

The output of the demodulator x,(t) (ideal demodulator followed by asimple low-pass network) is therefore given by the low-frequency signalcontained in lx (t)cos (m t-hb Using equation (10) yields:

2x (t)cos (w t+ [x,,(t) cos +jx (t)sin (COSCOS 2w t+sin sin 2m,.t)x,,(t) +j(cosk sin2w,tsin cs2 t)x (t). 13

Since the low-pass filter of the demodulator passes only low-frequencyterms of equation (13 the output is the function:

From the Laplace transform there results:

X (s) X,(s)cos +jX,,(s)sin 11( 5 c( j c) c( j c) bd (17) and usingX,,(s) and X (s) from equation (12) in equation (15) results in:

4 p( j q( (18) Thus:

4 4( 1( p( )+j q( (19) This is the low-frequency transfer functionequivalent of the carrier frequency channel of FIG. 4. This transferfunction allows design and analysis of the entire control system on aunified basis. Expanding equation (19 yields:

The demodulator reference phase angle 41,, is ordinarily set to zero.The term G (s) becomes: 8( 4( l( c( j c) c( j c) (21) Statement of theProblem of AC Network Compensation of AC Control Systems It has beenderived that the effect of the network in an AC channel upon thenon-carrier-frequency input signal is given by the equivalent transferfunction: UN 4( 1( c( +j c( -j-)] where G (s) is the ordinary voltagetransfer function of the network and d of G, (s) signifies ,,=0.

The problem of AC network compensation of AC control systems istherefore to provide the network G (s) which has the specified property:

ad- 4( 1( I A 'J'MH A J'M) (22) corresponding to the required G, (s). Itis known from electric network theory that it is impossible to satisfyequation (22) for all frequencies. Therefore, the problem is stated tosatisfy equation (22) within a finite band of frequencies: edU 4U 1UThus the problem is to find electric networks with a transfer functionapproximating G,,,(iw) within any accuracy over the desired band offrequencies where w w this is usually stated to mean satisfying the gainresponse within a constant and the phase response within a constant.(The first constant simply involves an amplifier adjustment, the secondconstant may be adjusted for in the demodulator motor.)

Consideration of the more general form of G (s) where the demodulatorphase angle is not equal to zero leads to more specific properties ofthe ideal AC network. Although the two properties of the ideal ACnetwork have been known for the over twenty years that the problem hasbeen before the engineering community, only narrow-band solutions havebeen found until this invention. From equation (19):

In order for the quadrature component to be zero (for s=ja); tu -w g m gol fin there results:

Since for a n6tW0l1( function o [i 5%) e 1i r where G, signifies complexconjugate of G equation 24) becomes:

e U t- 1= 6 U v+ 1 (24a) ew o This means that the gain response of thenetwork must have even symmetry about the carrier frequency and thephase response must have odd symmetry about its value at the carrierfrequency. The total equivalent transfer function becomes:

2( A ti e) bc or in terms of frequency response:

t [1' el 4 (25a) :40 e Li d- (25b) The properties which the network G(s), which solves the problem of wide-band AC network compensation of ACcontrol systems, should have are illustrated in FIG. 7. The frequencyresponses [6,(jw) I and G, .(jm) have even and odd symmetry,respectively, around the carrier frequency; the gain response and thephase response have the same shapes at a band around carrier frequencyas do the gain and phase response of the equivalent transfer functionfor a band around zero frequency.

Thus the AC network of this invention is an electrical network designedso as to yield an optimal degree of arithmetical symmetry in response,even symmetry in gain response and odd symmetry in phase angle responsefor a wide band of frequencies around the carrier frequency, that is,for (D -(Du m g m +m where w m and w is the carrier frequency. This, itis believed, is a breakthrough solution in the field of AC modulatedcontrol systems. The AC network solution found has the long soughtproperties required to improve the stability and performance of ACmodulated control systems. This means that wide band AC design is notpossible, that substantially greater accuracy in design is possible, andthat reduced power consumption and reduced demodulator motor heating ispossible.

NETWORK DESIGN IN ACCORDANCE WITH INVENTION The objective of the designin terms of electric network theory is to determine an AC network suchthat it has the same gain frequency response within a constant and thesame phase frequency response within a constant around the carrierfrequency as does a low frequency network around zero frequency; this isfor a finite band of frequencies, (D g (0 cu -Ho where m w and g m g a)By considering only minimum phase networks (networks with transferfunctions having zeros in the left half s-plane only) the design problemis stated in terms of only the gain characteristic (it is only necessaryto approximate the symmetrical gain characteristic):

The voltage transfer function of a passive network has the form:

where E is the output voltage and E is the input voltage, P (s) is apolynomial in s and P (s) is a polynomial in s. The voltage transferfunction of the network determines a relation between two characteristicimpedances of the network. For the characteristic opencircuit impedancesZ and Z the relation is T(s) =E /E,=Z ,/Z,,. Here any load impedance isdefined as internal to the network.

where P has even powers of s and sP has odd powers. From the identity+jBl a w,

the result is:

Thus, it is observed that the gain squared function of a passiveelectric network is a ratio of polynomials in even powers of omega (0).It is further observed that the design problem can e solved byapproximating even powers of omega by a ratio of even polynomials inomega one (m m r (m 2( More specifically, the non-impedancetransformation (with band frequency translating properties) arrived atis the following:

[This has the form,

where 21r (w, means 2(m, +d,) (m, +d (m, +d,,,) Equation (31) forseveral m values yields,

The properties of this transformation are derived as follows: Theproperties required for 0,,,(m,)' are two, (I) 0,,,(m +m & 10 (w -m g 1,ca he and (2) 0,,,(a) +w,) {L m -m The properties of 0, can bedetermined by examining 0,,(6 where (0 11:13,. This yields:

Therefore, it is evident that:

with an arbitrary degree of arithmetical symmetry with increasing m,since the second term of the denominator of (33) becomes arbitrarilysmall with increasing In for 0 5. '17, w l, yielding:

'and the numerator polynomial exclusive of 6, are

equal for powers of (01 less than 2m. The demonstration of this propertyresults from examining equation (32) and observing that the twopolynomials are identical except for the coefficients of 6,; therefore,property (3), that the approximation is optimal in this sense, isdemonstrated.

FIG. 6 illustrates an AC electrical network as contemplated by thisinvention and in the form of a resistance-capacitance, RC electricalnetwork which because of its configuration may be described as a twin Tnetwork. It is so named because the elements are connected in thegeneral shape of two Ts in series with a common input resistor r andterminated in a common load represented by resistor r One of the Tnetworks consists of series capacitors C and C connected: throughresistor r between input terminal 88 and output terminal 90 and resistorR, connected between the capacitors and common input and outputterminals 92 and 94. The other network consists of resistors R and R inseries with resistor r between input terminal 88 and output terminal 90and capacitor C connected between resistors R and R and common input andoutput terminals 92 and 94.

Keeping in mind that the purpose of the present invention is to providea desired correction or compensation for some signal condition, the ACmodulated network of the invention, as is the case with impedancenetworks in general, is intended to provide a signal modificationbetween the input and output terminals of the network. This modificationis generally referred to as a transfer function. This transfer functionor T(s) may be considered in terms of the ratio of the output voltage ofthe network, E, to input voltage E, or gain and phase angle of thenetwork.

By considering only minimum phase networks, networks with transferfunctions having zeros in the left half s-plane only, the design problemis stated in terms of only the gain characteristic since it is onlynecessary to approximate the symmetrical gain characteristic. Inaccordance with the present invention, an AC network is constructed toprovide the following gain and phase angle:

vg is a constant, and for real parameters, 0 b 0.5.

In terms of the actual network elements as they are labeled in th edrawings,

is satisfied.

Comparison of corresponding coefficients of powers of s in (35) and (36)results in the relations,

and

where and D From (39), R results,

where by choosing the parameters, p (R,+R /r,+r and p (R R- lr r tosatisfy the conditions,

From (40), C results after substitution for C, and C,. From (38),

symmetrical with frequency whereas the phase shift between input andoutput has an odd symmetry as shown by phase shift curve 98.

Networks of the character described have an arithmetical symmetry over asubstantial range around the carrier frequency, that is for the case PV-W W W +W where W W W is the carrier frequency, and W is the frequencycorresponding to the band width. This solution provides a breakthroughin the field of AC modulated control systems. The AC network determinedhas the long sought properties required to improve the stability andperformance of AC modulated control systems. This means thatcompensation networks for such systems can be designed to cover a muchwider band than previously believed possible. Further, this means thatrequired circuit response can be achieved with greater accuracy, withlower power consumption and with reduced demodulator and motor losses.More specifically, the invention enables construction of an AC networkwhich has the same gain frequency response and the same phase frequencyresponse within a constant range around the carrier frequency as does alow frequency network around zero frequency. This is, of course, for afinite band of frequencies wherein W W,, W W -I-W where W WC.

The resultant asymmetry for the twin T version of my invention where b,is taken as 0.4 is as follows. With a band width of 50 percent'of ZW thegain asymmetry at the edges is 3.14 percent as a maximum. Thus it can beseen that AC modulated control system networks another type ofderivative or lead characteristic which results from my invention is:

When the impedance Z, of FIG. 8 is taken as that of the network shown inFIG. 9, the result when the RLC element values shown therein aredetermined from (53) there is provided an optimal AC control systemnetwork. The network of FIG. 9 is a two section ladder network whereinthe first section 102 consists of a series circuit of resistor r, inseries with paralleled resistor R and capacitor C in the series leg ofthe section followed by resistor R and inductor L (in series) parallelwith resistor R and in series with paralleled capacitor C and resistor Rin the parallel leg of the section. The second section 104 of thenetwork consists of counterparts of the first section having the suffixa added to each counterpart designation. The network is terminated inseries resistor R and a parallel circuit consisting of resistor R andcapacitor C (in series) paralleled with resistor r,. A significantrelationship between component values is that the time constantrepresented by R C is substantially equal to R C and the time constantrepresented by R C is substantially equal to R C Y It has been foundthat when the present invention is applied to the ladder type network asshown in FIG. 9, that the asymmetry is as follows. With a band of 70percent of 2w, (carrier frequency), the gain asymmetry, at the edges, is2.02 percent as a maximum.

The result in asymmetry for the twin T embodiment of the invention shownin FIG. 6 when b is taken as 0.4 is as follows. With a band of a 50percent of 210 the gain asymmetry, at the edges, is 3.14 percent as amaximum. In either case, the AC control system networks obtained inaccordance with the present invention provide stabilization andcompensation properties over optimal band widths.

What is claimed is:

1. In an AC control circuit including an AC driven motor and motorcontrol means responsive to an input control signal impressed upon an ACcarrier and a mechanical input representative of the position of saidmotor, AC impedance network means connected in circuit between an outputof said motor control means and an input of said motor for providing apredetermined compensation to said control signal representative of afirst impedance transfer function acting on said control signalcomprising a plurality of electrical impedance elements connectedbetween an input and an output and being so interconnected and havingsuch values as to provide a second impedance transfer function whereinthe relationship between said first and second transfer functions isexpressed as: w (wf-l) l" r- )""l wherein w is representative of thecontrol signal frequency, w, is representative of the modulated controlsignal frequency, and m is a positive integer in the range of l toinfinity, and wherein said network means displays an arithmeticalsymmetry around the carrier frequency, being an even symmetry as to gainresponse and an odd symmetry as to phase response for a band width lessthan but substantially equal to twice the carrier frequency;

whereby said AC impedance network means accomplishes a wide band ACmodulated control effect which controls the signal on the modulatedcarrier in substantially the same way as a network having a said firstimpedance transfer function and adapted to operate directly on thecontrol signal.

2. In an AC modulated control circuit as set forth in claim I, summingmeans for selectively adding portions of the input to and output fromsaid AC impedance network means for providing said input to said motor.

3. In an AC modulated control circuit as set forth in claim 1 whereinsaid AC impedance network means comprises a four terminal ladder networkhaving at least one section comprising:

a series parallel RC network, and at least one section of the networkcomprising:

an RC network connected between a first input terminal and a firstoutput terminal; and

an RLC network and a second RC network connected in series with saidfirst named RC network to commonly connected second input and outputterminals and wherein the time constant of said RC networks aresubstantially identical.

4. In an AC modulated control circuit as set forth in claim I, whereinsaid AC impedance network comprises a four terminal twin T network witha series input resistor r, in one line, resistor r, across the outputterminals, where one T of the circuit is formed by resistors R; and R asthe top portion of the T and capacitor C connected between theintersection of resistors R and R to one input and one output terminalconnected together, and the other T of the circuit comprises capacitor Cand capacitor C in series and a resistor R is connected between saidcapacitors in series to said input and output terminals connectedtogether and wherein the electrical resistors and capacitors have valueswherein:

where D, V 2 b,(b,+2)"= (bf-1)] /(b1+2)", and b satisfies, 0 b 0.5 inthe network transfer function,

wherein the carrier frequency is the normalized frequency, w ==l.

a: a: a

UNITE?) PATFNT GFFiCE """T f-"T' if L. Lair 1 ii lei-"1 fin U11CUQRriQTlQN PATENT NO. 3,764,878 rmao October 9, 1973 lxvExTORk'S) VanA. McAuley 11 i5 cerizhee that are: apgems m the ab0ve-loemified patentand that said Letters Patent me heresy cwectec as shown below:

Column 4, lines 32-33, delete "From the Laplace transform of each side iof equation (3)".

Column4, line 34, change (first occurrence) to Column 4, line 34, change(second occurrence) co- 0 Column 4, line 37, change (first occurrence)to-- Column 4, line 37, change (second occurrence) co-ac Column 4,-1ine48, change co- Column 4, line 52, change to--v Column 4, line 53, changetor Column 4, line 53, after "jw add-)-. Column 4, line 62, change toColumn 4, line 65, change tO--ac Column 5, line 9, change "1" to-2--.

Column 5, line 12, change "cos .ZW tocos2w t-. Column 5, line 12, change"sin Zw to-sin2w t--.

Column 5, line 12, change "l" to--d S'EA'EEb' PATENT OFFICE CERTIFL'CA'CORRECTION PATENT NO. 3,764,878 omen October 9, 1973 Page 2 INVENTORtS)Van A. McAuley It is certified that error appears in'theabove-identified patent and that said Letters Patent are herebycorrected as 'shown below:

Column 5, line 13, delete "d" (first occurrence). Column 5, line 13,change "c"to-w 7 (5611mm 5, line 46, delete e y Column 5, line 46,change ..."jw cos"...to--jw )]cos-. (361mm 5, line 66, after equation 22add-- (s=jw Column 6, line 6, change '.'w to--w Column 6, line 44,change tO--4 Column 6, line 5-5, change to-L Column 7, line 6, change"not" to--no Column 7, line 58, change to Column 7, line 63, immediatelyafter "l (second occurrence) addand delete before Column 7, line 63,after "P add- Column 7, line 63, after "(ev)" delete Column 7, line 63,after "P (second occurrence) add-- Column 7, line 63, after "(66 deleteRATE-WT OFFZCE CEll iCiF'iCA'lE O ORRECTEON PATENT No. 1 3,764,878 DATEDOctober 9, 1973 Page 3 INVENTOMS) Van A. McAuley it is canted that errorappears In the above-idemified patent and that said Letters Patent arehereby corrected as shown below:

Column 8, line 1, change "e" tobe--.

Column 8, line 5, change to--=--.

Column 8, line 5, after 1,1 add)-. Column 8, line 16, delete "(w +m)"and add therefor --(w +d Column 8, line 17, after "w +d add--]-anddelete Column 8, line 21, after "=(w" ad cum 8, 1111522, after "=(w" addColumn 8, line 22, after "(2w" (first occurrence) add- Colunm 8, line22, after "+l2w" add Column 8, line 23, after "=(w" addafter (2w" addafter "+30w" (first occurrence) ad and after "+30w' (second occurrence)add- Column 8, line 24, after "=(w" addafter (2w" addafter +56w" (firstoccurrence) add after "+l40w" add and after "+56 w" (second occurrence)add Column 8, line 52, add- (before the equation and delete Column 8,line 60, delete "W and substitute therefor-$ I t l I UNITED 51211115P111111 "1" OFFICE CERTIFICATE 0 I CORRECTION PATENT NO. 3,7 4,878 fDATED October 9, 1973 Page 4 INVEfL tur- Van A. McAuley I it rscertified that my SIEIIET; 2 .;e--t:u:1trtied patent and that saidLetters Patent are hereby corrected as 3516M? Column 9, line 2, delete"W and add--T/r' Column 9, line 65, change [[b (b +2) b -l)]] to-- [b (b+2 (b -1 n Column 10, l1ne 20, change "r +r +r r to r +r +r r Column 10,line 46, after "[r r (R +R add--/-.

Column 11, line 43, delete "c (R +R (R R )R +l/(R R C and substitutethereforC =[(R +R (R R5)]R C +1/ (R R C Column 11, line 53, delete [l+R(R and substitute- [l+R /R Column 11, line 66, after "4m m delete "/2mand add outside the radical)/Zm Column 13, line 14, delete "R C andsubstituteR C 511K385 PAIENE OFFICE CER ilFlCe-JM OE CORREC'EIGN PATENT0. 1 3,764,878 Page 5 DATED October 9, 1973 lNVENTORkb) Van A. McAuleyit is cemfied that enor appears m the above-identified patent and thatsaid Letters Patent are hereby corrected as shswn below:

comm 14, line 38, after bf-1 add Column 14, line 53, change r to-- 1' 12 1 2 1 3 1+ 1 3 f z f z Column 15, line 4, after add--)-; after "2111delete "1".

Column 15, line 5, after "where addm Signed and Sealed this eighteenth D3) of November 1 975 [SEAL] Altesr:

RUTH C. MASON C. MARSHALL DANN jj'im'r (HHIHUSSIHHUV nl'Pulcnls andTrademarks

1. In an AC control circuit including an AC driven motor and motorcontrol means responsive to an input control signal impressed upon an ACcarrier and a mechanical input representative of the position of saidmotor, AC impedance network means connected in circuit between an outputof said motor control means and an input of said motor for providing apredetermined compensation to said control signal representative of afirst impedance transfer function actIng on said control signalcomprising a plurality of electrical impedance elements connectedbetween an input and an output and being so interconnected and havingsuch values as to provide a second impedance transfer function whereinthe relationship between said first and second transfer functions isexpressed as: w2m (w121) 2m/( (w1+1)2m + (w1-1)2m) wherein w isrepresentative of the control signal frequency, w1 is representative ofthe modulated control signal frequency, and m is a positive integer inthe range of 1 to infinity, and wherein said network means displays anarithmetical symmetry around the carrier frequency, being an evensymmetry as to gain response and an odd symmetry as to phase responsefor a band width less than but substantially equal to twice the carrierfrequency; whereby said AC impedance network means accomplishes a wideband AC modulated control effect which controls the signal on themodulated carrier in substantially the same way as a network having asaid first impedance transfer function and adapted to operate directlyon the control signal.
 2. In an AC modulated control circuit as setforth in claim 1, summing means for selectively adding portions of theinput to and output from said AC impedance network means for providingsaid input to said motor.
 3. In an AC modulated control circuit as setforth in claim 1 wherein said AC impedance network means comprises afour terminal ladder network having at least one section comprising: aseries parallel RC network, and at least one section of the networkcomprising: an RC network connected between a first input terminal and afirst output terminal; and an RLC network and a second RC networkconnected in series with said first named RC network to commonlyconnected second input and output terminals and wherein the timeconstant of said RC networks are substantially identical.
 4. In an ACmodulated control circuit as set forth in claim 1, wherein said ACimpedance network comprises a four terminal twin T network with a seriesinput resistor r1 in one line, resistor r2 across the output terminals,where one T of the circuit is formed by resistors R3 and R1 as the topportion of the T and capacitor C2 connected between the intersection ofresistors R3 and R1 to one input and one output terminal connectedtogether, and the other T of the circuit comprises capacitor C3 andcapacitor C1 in series and a resistor R2 is connected between saidcapacitors in series to said input and output terminals connectedtogether and wherein the electrical resistors and capacitors have valueswherein: